Geodesic
ON GROUPS WITH TWO ISOMORPHISM CLASSES OF DERIVED SUBGROUPS
Glasgow mathematical journal, Tome 55 (2013) no. 3, pp. 655-668

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DOI

The structure of groups which have at most two isomorphism classes of derived subgroups ($\mathfrak{D}$2-groups) is investigated. A complete description of $\mathfrak{D}$2-groups is obtained in the case where the derived subgroup is finite: the solution leads an interesting number theoretic problem. In addition, detailed information is obtained about soluble $\mathfrak{D}$2-groups, especially those with finite rank, where algebraic number fields play an important role. Also, detailed structural information about insoluble $\mathfrak{D}$2-groups is found, and the locally free $\mathfrak{D}$2-groups are characterized.
DOI : 10.1017/S0017089512000821
Mots-clés : Primary 20F14 
LONGOBARDI, PATRIZIA; MAJ, MERCEDE; ROBINSON, DEREK J. S.; SMITH, HOWARD. ON GROUPS WITH TWO ISOMORPHISM CLASSES OF DERIVED SUBGROUPS. Glasgow mathematical journal, Tome 55 (2013) no. 3, pp. 655-668. doi: 10.1017/S0017089512000821
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     title = {ON {GROUPS} {WITH} {TWO} {ISOMORPHISM} {CLASSES} {OF} {DERIVED} {SUBGROUPS}},
     journal = {Glasgow mathematical journal},
     pages = {655--668},
     year = {2013},
     volume = {55},
     number = {3},
     doi = {10.1017/S0017089512000821},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089512000821/}
}
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